Permutation Practice Questions

Master GMAT Permutation with comprehensive practice questions. Build your quantitative reasoning skills through detailed explanations and strategic practice.

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Question 1 of 5 Medium

How many different anagrams can you make for the word GMAT? How many different anagrams can you make for the word MATHEMATICS?

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Correct Answer: C

The word GMAT has 4 distinct letters (G, M, A, T). Since all letters are different, the number of anagrams is \(4! = 24\). The word MATHEMATICS has 11 letters total. Without considering repetitions, we could arrange them in \(11!\) ways. However, the letters M, A, and T each appear twice in MATHEMATICS. When a letter is repeated, swapping the identical letters creates the same arrangement, so we must divide by the factorial of the number of repetitions for each repeated letter. Since M appears 2 times, A appears 2 times, and T appears 2 times, we divide by \(2!\) for each: \[\frac{11!}{2! \times 2! \times 2!}\] Therefore, the number of different anagrams for GMAT is \(4!\) and for MATHEMATICS is \(\frac{11!}{2! \times 2! \times 2!}\).

Question 2 of 5 Medium

There are 2 black balls, one red ball and one green ball, identical in shape and size. How many different linear arrangements can be generated by arranging these balls?

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Correct Answer: A

Total items \( n=4 \).
Identical items: 2 black balls.

Permutations = \( \frac{4!}{2!} = \frac{24}{2} = 12 \).

The correct answer is A.

Question 3 of 5 Medium

A book store has received 8 different books, of which \( \frac{3}{8} \) are novels, \( 25\% \) are study guides and the remaining are textbooks. If all books must be placed on one shelf displaying new items and if books in the same category have to be shelved next to each other, how many different arrangements of books are possible?

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Correct Answer: E

Number of Novels = \( \frac{3}{8} \times 8 = 3 \).
Number of Study Guides = \( 0.25 \times 8 = 2 \).
Number of Textbooks = \( 8 - 3 - 2 = 3 \).

Arrangement of 3 categories = \( 3! = 6 \).
Internal arrangements:
Novels: \( 3! = 6 \).
Study Guides: \( 2! = 2 \).
Textbooks: \( 3! = 6 \).

Total arrangements = \( 6 \times 6 \times 2 \times 6 = 432 \).

The correct answer is E.

Question 4 of 5 Medium

The organizers of a week-long fair have hired exactly five security guards to patrol the fairgrounds at night for the duration of the event. Exactly two guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different pairs of guards will be available to patrol the fairgrounds on the following Saturday night?

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Question 5 of 5 Medium

You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter?

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